Articles containing proofs | Real transcendental numbers | Diophantine approximation | Irrational numbers | Mathematical constants
In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exists a pair of integers (p, q) with q > 1 such that . Liouville numbers are "almost rational", and can thus be approximated "quite closely" by sequences of rational numbers. They are precisely those transcendental numbers that can be more closely approximated by rational numbers than any algebraic irrational number. In 1844, Joseph Liouville showed that all Liouville numbers are transcendental, thus establishing the existence of transcendental numbers for the first time.It is known that π and e are not Liouville numbers. (Wikipedia).
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From playlist Complex Numbers
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From playlist Recent videos
Alexander Belavin - The correlation numbers in Minimal Liouville gravity
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Nikos Frantzikinakis: Ergodicity of the Liouville system implies the Chowla conjecture
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Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys
From playlist Complex Numbers
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From playlist Jason Miller - Equivalence of Liouville quantum gravity and the Brownian map